Matrix Operations for Engineers and Scientists An Essential Guide in Linear Algebra /

• Κύριος συγγραφέας: Jeffrey, Alan (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Dordrecht : Springer Netherlands : Imprint: Springer, 2010.
• Θέματα: Physics.; Matrix theory.; Algebra.; Differential equations.; Applied mathematics.; Engineering mathematics.; Mathematical Methods in Physics.; Appl.Mathematics/Computational Methods of Engineering.; Linear and Multilinear Algebras, Matrix Theory.; Ordinary Differential Equations.

Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. Ho...

Πίνακας περιεχομένων:

• 1. MATRICES AND LINEAR SYSTEMS
• 1.1 Systems of Algebraic Equations
• 1.2 Suffix and Matrix Notation
• 1.3 Equality, Addition and Scaling of Matrices
• 1.4 Some Special Matrices and the Transpose Operation. Exercises
• 1 2. DETERMINANTS AND LINEAR SYSTEMS
• 2.1 Introduction to Determinants and Systems of Equation
• 2.2 A First Look at Linear Dependence and Independence
• 2.3 Properties of Determinants and the Laplace Expansion Theorem
• 2.4 Gaussian Elimination and Determinants
• 2.5 Homogeneous Systems and a Test for Linear Independence
• 2.6 Determinants and Eigenvalues. Exercises
• 2 3. MATRIX MULTIPLICATION, THE INVERSE MATRIX AND THE NORM
• 3.1 The Inner Product, Orthogonality and the Norm 3.2 Matrix Multiplication
• 3.3 Quadratic Forms
• 3.4 The Inverse Matrix
• 3.5 Orthogonal Matrices 3.6 Matrix Proof of Cramer’s Rule
• 3.7 Partitioning of Matrices. Exercises 34. SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
• 4.1 The Augmented Matrix and Elementary Row Operations
• 4.2 The Echelon and Reduced Echelon Forms of a Matrix
• 4.3 The Row Rank of a Matrix 4.4 Elementary Row Operations and the Inverse Matrix
• 4.5 LU Factorization of a Matrix and its Use When Solving Linear Systems of Algebraic Equations
• 4.6 Eigenvalues and Eigenvectors. Exercises
• 4 5. EIGENVALUES, EIGENVECTORS, DIAGONALIZATION, SIMILARITY AND JORDAN FORMS
• 5.1 Finding Eigenvectors
• 5.2 Diagonalization of Matrices
• 5.3 Quadratic Forms and Diagonalization
• 5.4 The Characteristic Polynomial and the Cayley-Hamilton Theorem
• 5.5 Similar Matrices 5.6 Jordan Normal Forms
• 5.7 Hermitian Matrices. Exercises.-56. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
• 6.1 Differentiation and Integration of Matrices
• 6.2 Systems of Homogeneous Constant Coefficient Differential Equations
• 6.3 An Application of Diagonalization 6.4 The Nonhomogeneeous Case
• 6.5 Matrix Methods and the Laplace Transform
• 6.6 The Matrix Exponential and Differential Equations. Exercises
• 6.7. AN INTRODUCTION TO VECTOR SPACES
• 7.1 A Generalization of Vectors
• 7.2 Vector Spaces and a Basis for a Vector Space
• 7.3 Changing Basis Vectors
• 7.4 Row and Column Rank
• .5 The Inner Product
• 7.6 The Angle Between Vectors and Orthogonal Projections
• 7.7 Gram-Schmidt Orthogonalization
• 7.8 Projections
• 7.9 Some Comments on Infinite Dimensional Vector Spaces. Exercises 78. LINEAR TRANSFORMATIONS AND THE GEOMETRY OF THE PLANE
• 8.1 Rotation of Coordinate Axes
• 8.2 The Linearity of the Projection Operation
• 8.3 Linear Transformations 8.4 Linear Transformations and the Geometry of the Plane. Exercises
• 8Solutions to all Exercises.